Epistemic Possibility

Here, I try to analyze the notion of epistemic possibility.*

[* Based on: “Epistemic Possibility,” Synthese 156 (2007): 119-42.]

1. The Idea of Epistemic Possibility

According to philosophers, there are multiple different kinds of “possibility”, including metaphysical possibility, which might be distinct from logical possibility; physical possibility; and epistemic possibility.

Example: I tell you I’ve lost my phone. You say, “Could it be in the Starbucks?” That “could” refers to epistemic possibility. Obviously it’s logically, metaphysically, and physically possible for the phone to be in the Starbucks, but those are all irrelevant. If I know the phone isn’t there (for example, I already checked there, or I know I had it after the last time I left Starbucks), then I should answer, “No, it can’t be there” or “No, it’s definitely not there.” “It’s definitely not there” is the contradictory of “It might be there.”

I decided to figure out exactly what this kind of “could” really means.

2. Seven False Analyses

It’s surprisingly hard to say what “might” (in the epistemic sense) means. Let’s try . . .

Definition 1: P is epistemically possible for S = S does not know that ~P.

Problem: Consider this case:

Rigel 7: Sam knows nothing of astronomy and hence has no awareness of the star Rigel, nor any of the planets orbiting it. One day, Sam looks at his couch, sees it normally and sees nothing on it. Mary (who happens to know about Rigel and that it has 7 planets orbiting it) says: “For all Sam knows, Rigel 7 is on his couch” (or: “It’s possible for Sam that Rigel 7 is on his couch”).

Mary’s utterance is obviously false. Yet according to Definition 1, it would be true, since Sam doesn’t know that Rigel 7 isn’t on the couch, since Sam doesn’t even believe that, since he doesn’t even have a concept of Rigel 7.

Definition 2: P is epistemically possible for S = P is consistent with everything S knows.

This would get the Rigel 7 case right, since Sam knows some stuff (e.g., that there is nothing on his couch) that is incompatible with Rigel 7’s being on his couch. But now consider:

Complicated Proof: Sam goes through a complicated, 5-page-long proof, which is, in actual fact, completely correct. However, Sam hasn’t checked it carefully, he knows he has sometimes made errors in mathematical reasoning in the past, so he rationally takes it to be pretty likely that there are some errors in this proof. Sam says, of the proof’s conclusion, “This might be wrong. I better check it over.”

Sam’s statement is correct; for all he knows, the proof might be wrong. But Definition 2 implies the opposite: since the proof is in fact correct, and (as we assume) Sam knows its premises (which are some self-evident axioms), the negation of the conclusion isn’t in fact consistent with everything Sam knows.

Definition 3: P is epistemically possible for S = If S were to consider whether P, S would not know that ~P.

This one correctly accommodates both Rigel 7 (implying that it’s impossible that Rigel 7 is on the couch) and Complicated Proof (implying that it’s possible that the proof is mistaken). But now consider:

Unconscious Sam: Sam is currently unconscious. Mary says of him, “It’s epistemically impossible for Sam that he is unconscious.”

Mary’s statement is false (something that’s true can’t be epistemically impossible!). But Definition 3 makes it true, because if Sam were to consider whether he was conscious, he would have to be conscious. Which means that he would then know introspectively that he was conscious.

Definition 4: P is epistemically possible for S = S does not know ~P, nor would any practicable investigations by S establish ~P.

This might get the Unconscious Sam case right, if you say that it’s not practicable for Sam to do any investigations, since he’s currently unconscious.

But this gets the Complicated Proof case wrong. In that case, Sam could check the proof over carefully, in which case he would establish that the proof isn’t mistaken. Nevertheless, since he hasn’t in fact done so, it is possible for him that the proof is wrong.

Definition 5: P is epistemically possible for S = The probability of P on S’s evidence is nonzero.

Problem: This also mishandles the Complicated Proof case. According to standard probability theory, given that the proof is in fact correct, the probability of its conclusion would be 1. So on Definition 5, it would be epistemically impossible that the conclusion is wrong.

Definition 6: P is epistemically possible for S = It is metaphysically possible for someone to have the kind and degree of justification that S has for ~P, for a false proposition.

This gets the Complicated Proof right, because the kind & degree of justification that Sam has in that case is the same as the kind & degree of justification he would have in a case where he did an equally complicated proof that contained an error.

However, this gets wrong cases like the following:

Landing: I’m flying into Denver. Upon landing, I call Iskra and say, “I’ve landed.” She says, “Might you still be in the air?” I say, “No, I’m looking out the window right now. We’re definitely on the ground.”

My statement here is totally reasonable. Yet it is metaphysically possible for someone to have this kind of justification and yet be mistaken – e.g., I could, as a total fluke, be having an incredibly realistic hallucination of having just landed. So Definition 6 wrongly implies that I should say, “Yes, obviously I might still be in the air. I also might be on Pluto.”

Similarly, in the case where I lost my phone, and I know I had it after I left the Starbucks because I texted Iskra on it, I would still have to say, “Yeah, it might be in the Starbucks.” That’s silly.

Definition 7: P is epistemically possible for S = S does not know that ~P, and there is no relevant way by which S could come to know ~P.

This one is based on an article by Keith DeRose. What count as “relevant” ways of knowing is thought to vary depending on conversational context, and DeRose does not provide precise rules for how this varies.

My problem with this is just that it is too easy. For almost any S and P, where P is in fact false, there will be some ways in which S could come to know ~P. (If P is true, then there will of course be no way of coming to know ~P.) You can make Definition 7 accommodate either the judgment that P is possible for S or the judgment that P is not possible, depending on whether you rule those ways of knowing “relevant” or not. So Definition 7 is not informative enough to be helpful.

3. A Pretty Good Analysis

Here’s a better account.

Definition 8: P is epistemically possible for S = P isn’t epistemically impossible for S.

P is epistemically impossible for S =

a.       P is false;

b.       S has justification for ~P adequate for dismissing P; and

c.       S’s justification for ~P is Gettier-proof.

Condition (c) refers to whatever condition (beyond justified, true belief) is needed to eliminate Gettier cases. E.g., take the case where someone coincidentally forms a correct belief by looking at a stopped clock. They have a justified, true belief, but they don’t know what time it is. Presumably, they fail some fourth condition on knowledge. Whatever that is, that condition would go into part (c) of the above definition of epistemic impossibility.

Now about condition (b). Dismissal, here, is a strong form of rejection. When you “dismiss” a possibility, you refuse to take it seriously; thus, you would treat it as irrelevant to practical deliberations, and irrelevant to the project of figuring out what’s true. E.g., when I’m looking for the salsa in the supermarket, and you ask me how I know I’m not a brain in a vat, I should just laugh that off. I shouldn’t start seriously deliberating about whether I’m a BIV.

As that example shows, you can be perfectly reasonable in dismissing a possibility even though it has a nonzero probability and even though, if it were true, that would totally mess up the rest of your reasoning and decision-making. It can be sufficiently improbable that it just doesn’t make sense to waste time thinking seriously about it.

So that’s my proposal for what epistemic possibility is. I claim that this gets all of the above cases right.

Rigel 7: It’s epistemically impossible for Sam that Rigel 7 is on the couch, because (a) it is not on the couch, (b) Sam has justification for denying that Rigel 7 is on the couch (namely, his sensory experience of the couch) which would be strong enough to justify dismissing the possibility that Rigel 7 is on the couch, and (c) he’s not in a Gettier case.

Complicated Proof: It’s not epistemically impossible that the proof’s conclusion is wrong, because (condition b) Sam doesn’t have justification strong enough for dismissing the possibility that the proof contains errors.

Unconscious Sam: It’s not epistemically impossible for Sam that he’s unconscious, because (condition a) he is in fact unconscious.

Landing: It’s epistemically impossible for me that I’m still in the air, because (a) I’m on the ground, (b) I have justification for this (viz. seeing that the plane is on the ground) that is good enough to make it reasonable for me to refuse to take seriously that I’m still in the air, and (c) I’m not in a Gettier case.

Is this, finally, the correct analysis? Well, knowing the history of epistemology, probably not; there are probably some counterexamples somewhere. But Definition 8 is still pretty close to correct, and it does better than Definitions 1-7.